The output of our reduction algorithm depends on the choice of a tropical equilibration solution.
Changing this solution may lead to different timescale orderings of the variables, truncated systems, approximate conservation laws and reduced models. However,
continuous branches of tropical solutions lead to the
same truncated systems, approximate conservation laws and
ordering of timescales. A branch of tropical equilibation solutions corresponds to a polyhedral domain in the space of logarithms
of species concentrations [1]}.
Furthermore, the validity of a given reduction can be extended to neighborhoods of such
polyhedra in logarithms of species concentrations.
For these reasons, the
reductions based on orders of magnitude
comparison (including those discussed in this paper) are
robust
[2]}, [3]}, [4]}.
However, biochemical CRNs are often
excitable and their trajectories explore very large
domains of the species concentrations space.
In such cases, the CRN may change the
branch of tropical solutions several times
along the same trajectory. Thus,
scalings, truncated systems and even approximate
conservation laws may change and several different reductions
must be used along the same trajectory
[5]}, [6]}, [1]}.
The study of switching between different reduced models asks
for different mathematical methods such as
blow-ups [8]} and
will be treated in future work.
